A180046 a(n+1) = a(n-3) + a(n-2) - a(n-1) + a(n) starting with 1, 2, 3, 4.

1, 2, 3, 4, 4, 5, 8, 11, 12, 14, 21, 30, 35, 40, 56, 81, 100, 115, 152, 218, 281, 330, 419, 588, 780, 941, 1168, 1595, 2148, 2662, 3277, 4358, 5891, 7472, 9216, 11993, 16140, 20835, 25904, 33202, 44273, 57810, 72643, 92308, 121748, 159893, 203096, 257259

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,-1,1,1).

Formula

G.f.: -x*(1+x)*(2*x^2+1)/(-1+x-x^2+x^3+x^4). - R. J. Mathar, Aug 14 2010

a(n) = (-1)^(n)*(A100329(n-1)-A100329(n)-2*A100329(n-2)+2*A100329(n-3)) with A100329(-1) = A100329(-2) = 0. - Johannes W. Meijer, Jul 06 2011

Example

1 2 3 4 (by definition); 1 + 2 - 3 + 4 = 4, 2 + 3 - 4 + 4 = 5, 3 + 4 - 4 + 5 = 8.

Mathematica

LinearRecurrence[{1, -1, 1, 1}, {1, 2, 3, 4}, 50] (* Harvey P. Dale, Mar 18 2015 *)

Prog

(PARI) Vec(x*(1+x)*(2*x^2+1)/(1-x+x^2-x^3-x^4)+O(x^99)) \\ Charles R Greathouse IV, Jul 06 2011
(Haskell)
import Data.List (zipWith4)
a180046 n = a180046_list !! (n-1)
a180046_list = [1..4] ++ zipWith4 (((((+) .) . (+)) .) . (-))
                          (drop 3 a180046_list) (drop 2 a180046_list)
                            (tail a180046_list) a180046_list
-- Reinhard Zumkeller, Oct 08 2014

Crossrefs

Cf. A100329.

Sequence in context: A103750 A036805 A036804 * A008329 A064558 A178031

Adjacent sequences: A180043 A180044 A180045 * A180047 A180048 A180049

Keyword

nonn,easy

Author

Ian Stewart, Aug 08 2010

Extensions

More terms from R. J. Mathar, Aug 14 2010

Name edited by Michel Marcus, Feb 20 2025

Status

approved